Cops arrested a rape suspect Tuesday after he checked himself in at a psych ward under his own name — which he had revealed to his alleged victim before she was raped in Central Park early Sunday, sources said.

Omar Hoist, 32, was located at Metropolitan Hospital, where cops tracked him after putting out his name and picture Monday.

He allegedly followed the woman into the park and attacked her, a law-enforcement source said.

Hoist allegedly stalked his victim along East 88th Street at Fifth Avenue, near the Guggenheim Museum, at about 3:30 a.m. Sunday.

The suspect struck up a conversation and they entered the park together. They were seen together on video as they entered the park, sources said.

They later sat down on a bench, where Hoist allegedly attacked her and fled.

He was charged at the Central Park Precinct station house Tuesday night with rape, assault and strangulation.